Mia tosses a a ball to her dog. The function -0.5(x-2)² + 8 represents the ball path.

The correct answer is: C = 6

1.What does the vertex form of the function tell you about the situation?
Solution:- The standard quadratic form is ax²+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)²+k.
In both forms, y is the y-coordinate, x is the x-coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (−a).
The vertex form of the equation also gives you the parabola's vertex: (h,k).
This vertex is the highest point on the trajectory of the ball tossed by mia.
2.What does the standard form of a function tell you about the situation?
Solution:- The standard quadratic form is ax²+bx+c=y
In this the term c gives us the y-intercept of the curve
In the given case it gives the height from which the ball is thrown.

-0.5(x-2)² + 8 = y

- 0.5( x²+ 4 – 4x) + 8 = y

-0.5x² – 2 + 2x + 8 = y

-0.5x² + 2x + 6 = y

C = 6
Which is height from which the ball is thrown.